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Gravity currents with residual trapping

  • M. A. HESSE (a1), F. M. ORR (a1) and H. A. TCHELEPI (a1)
Abstract

Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The residual acts as a loss term that reduces the current volume continuously. In the limit of a horizontal aquifer, the interface shape is self-similar at early and at late times. The spreading of the current and the decay of its volume are governed by power-laws. At early times the exponent of the scaling law is independent of the residual, but at late times it decreases with increasing loss. Owing to the self-similar nature of the current the volume does not become zero, and the current continues to spread. In the hyperbolic limit, the leading edge of the current is given by a rarefaction and the trailing edge by a shock. In the presence of residual trapping, the current volume is reduced to zero in finite time. Expressions for the up-dip migration distance and the final migration time are obtained. Comparison with numerical results shows that the hyperbolic limit is a good approximation for currents with large mobility ratios even far from the hyperbolic limit. In gently sloping aquifers, the current evolution is divided into an initial near-parabolic stage, with power-law decrease of volume, and a later near-hyperbolic stage, characterized by a rapid decay of the plume volume. Our results suggest that the efficient residual trapping in dipping aquifers may allow CO2 storage in aquifers lacking structural closure, if CO2 is injected far enough from the outcrop of the aquifer.

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Bachu S. & Bennion B. 2007 Effects of in-situ conditions on relative permeability characteristics of CO2–brine systems. Environ. Geol. doi 10.1007/s00254-007-0946-9.
Barenblatt G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press.
Bear J. 1972 Dynamics of Fluids in Porous Media. Elsevier.
Bear J. & Ryzhik V. 1998 On displacement of NAPL lenses and plumes in a phreatic aquifer. Transport Porous Med. 33, 227255.
Benson S. M., Tomutsa L., Silin D. & Kneafsey T. 2006 Core scale and pore scale studies of carbon dioxide migration in saline formations. In Proc. GHGT-8, Trondheim, Norway.
Bickle M., Chadwick A., Huppert H. E., Hallworth M. & Lyle S. 2007 Modelling carbon dioxide accumulation at Sleipner: implications for underground carbon storage. Earth Planet. Sci. Lett. 255, 164176.
Ennis-King J. & Paterson L. 2002 Engineering aspects of geological sequestration of carbon dioxide. In Asia Pacific Oil and Gas Conf. and Exhibition, Melbourne, Australia.
Ennis-King J., Preston I. & Paterson L. 2005 Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. Phys. Fluids 17 (8), 084107.
Hassanzadeh H., Pooladi-Darvish M. & Keith D. W. 2007 Scaling behavior of convective mixing, with application to geological storage of CO2. AIChE J. 53 (5), 11211131.
Hesse M. A., Tchelepi H. A. & Orr F. M. Jr 2006 Scaling analysis of the migration of CO2 in saline aquifers. In SPE Annu. Tech. Conf. and Exhibition, San Antonio, TX.
Hesse M. A., Riaz A. & Tchelepi H. A. 2007 a Convective dissolution of CO2 in saline aquifers. Geochim. Cosmochim. Acta 71 (15), A401.
Hesse M. A., Tchelepi H. A., Cantwell B. J. & Orr F. M. Jr 2007 b Gravity currents in horizontal porous layers: transition from early to late self-similarity. J. Fluid Mech. 577, 363383.
Holloway S & Savage D. 1993 The potential for aquifer disposal of carbon-dioxide in the UK. Energy Convers. Manage. 34 (9–11), 925932.
Huppert H. E. & Woods A. W. 1995 Gravity-driven flows in porous media. J. Fluid Mech. 292, 5569.
Ide S. T., Jessen K. & Orr F. M. Jr 2007 Storage of CO2 in saline aquifers: effects of gravity, viscous, and capillary forces on amount and timing of trapping. Intl J. Greenh. Gas Control 1 (4), 481491.
Juanes R., Spiteri E. J., Orr F. M. Jr & Blunt M. J. 2006 Impact of relative permeability hysteresis on geological CO2 storage. Water Resour. Res. 42 (W12418), 113.
Kochina I. N., Mikhailov N. N. & Filinov M. V. 1983 Groundwater mound damping. Intl J. Engng Sci. 21, 413421.
Koperna G. J. & Kuuskraa V. A. 2006 Assessing technical and economic recovery of oil resources in residual oil zones. Tech. Rep. Advanced Resources International, 4501 Fairfax Drive, Suite 910, Arlington, VA 22203 USA.
Kumar A., Ozah R., Noh M., Pope G. A., Bryant S., Sepehrnoori K. & Lake L. W. 2005 Reservoir simulation of CO2 storage in deep saline aquifers. Soc. Petrol. Engrs J. September pp. 336–348.
Leveque R. J. 2002 Finite Volume Methods for Hyperbolic Problems. Cambridge University Press.
Lindeberg E. & Wessel-Berg D. 1997 Vertical convection in an aquifer column under a gas cap of CO2. Energy Conserv. Manage. 38, SS229SS234.
Lister J. R. 1992 Viscous flows down an inclined plane from point and line sources. J. Fluid Mech. 242, 631653.
Lyle S., Huppert H. E., Hallworth M., Bickle M. & Chadwick A. 2005 Axisymmetric gravity currents in a porous medium. J. Fluid Mech. 543, 293302.
Metz B., Davidson O., de Coninck H., Loos M. & Meyer L. (ed.) 2006 Special Report on Carbon Dioxide Capture and Storage. Cambridge University Press.
Michael K., Bachu S., Buschkuehle B. E., Haug K., Grobe M. & Lytviak A. T. 2006 Comprehensive characterization of a potential site for CO2 geological storage in central Alberta, Canada. In Proc. CO2SC Symp. 2006, Berkeley, CA.
Mo S., Zweigel P., Lindeberg E. & Akervoll I. 2005 Effect of geologic parameters on CO2 storage in deep saline aquifers. In SPE Eurospec/EAGE Annu. Conf. Madrid, Spain.
Nicot J.-P. 2007 Evaluation of large-scale carbon storage on fresh-water sections of aquifers: a Texas study. Intl J. Greenh. Gas Control (in press).
Nordbotten J. M., Celia M. A. & Bachu S. 2005 Injection and storage of CO2 in deep saline aquifers: analytical solution for the CO2 plume evolution during plume injection. Transport Porous Med. 58, 339360.
Riaz A. & Meiburg E. 2004 Linear stability of radial displacements in porous media: influence of velocity-induced dispersion and concentration-dependent diffusion. Phys. Fluids 16 (10), 3592.
Riaz A. & Tchelepi H. A. 2006 Numerical simulation of immiscible two-phase flow in porous media. Phys. Fluids 18 (014104).
Riaz A., Hesse M., Tchelepi H. & Orr F. M. Jr 2006 Onset of convection in a gravitationally unstable, diffusive boundary layer in porous media. J. Fluid Mech. 548, 87111.
Saffman P. G. & Taylor G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more visous fluid. Proc. R. Soc. Lond. A 245, 312329.
Vella D. & Huppert H. E. 2006 Gravity currents in a porous medium at an inclined plane. J. Fluid Mech. 555, 353362.
Verdon J. & Woods A. W. 2007 Gravity driven reacting flows in a confined porous aquifer. J. Fluid Mech. 588, 2941.
Yortsos Y. C. 1995 A theoretical analysis of vertical flow equilibrium. Transport Porous Med. 18, 107129.
Yortsos Y. C. & Hickernell F. J. 1989 Linear stability of immiscible displacement in porous media. SIAM J. Appl. Maths 49, 730748.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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